We propose an experimental scheme to probe the contribution of a single Dirac cone to the Hall conductivity as a half-odd topological number sequence. In the scheme, the quantum anomalous Hall effect in graphene is simulated with cold atoms trapped in an optical lattice and subjected to a laser-induced non-Abelian gauge field. By tuning the laser intensity to change the gauge flux, the energies of the four Dirac points in the first Brillouin zone are shifted from each other and the contribution of the single Dirac cone to the total atomic Hall conductivity is manifested. We also show that the atomic Hall numbers can be experimentally probed with atomic density profile measurements.

Representing a strongly interacting multiparticle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. A detailed comparison between finite Hilbert space calculations and exact results for up to five particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground-state energies, the low-lying excitation spectrum, density profile, and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.

The accumulation of atoms in the lowest energy level of a trap and the subsequent out coupling of these atoms is a realization of a matter-wave analog of a conventional optical laser. Optical random lasers require materials that provide optical gain but, contrary to conventional lasers, the modes are determined by multiple scattering and not a cavity. We show that a Bose-Einstein condensate can be loaded in a spatially correlated disorder potential prepared in such a way that the Anderson localization phenomenon operates as a bandpass filter. A multiple scattering process selects atoms with certain momenta and determines laser modes which represents a matter-wave analog of an optical random laser.

We study a square plaquette of four optical microtraps containing ultracold ${}^{87}$Rb atoms in the $F=1$ hyperfine state. In the presence of an external resonant magnetic field, the dipolar interactions couple the initial $m_F=1$ component to other Zeeman sublevels. This process is a generalization of the Einstein–de Haas effect to the case when the external potential has only $C_4$ point symmetry. We observe that vortex structures appear in the initially empty $m_F=0$ state. Topological properties of this state arise due to competition between the local axial symmetry of the individual trap and the discrete symmetry of the plaquette. For deep microtraps vortices are localized at individual sites, whereas for shallow traps only one discrete vortex appears in the plaquette. States created in these two opposite cases have different topological properties related to $C_4$ point symmetry.

We develop a theory for pulses propagating in normal dispersion fiber amplifiers with constant and varying gain, and for dispersion-decreasing fibers, including the effect of third-order dispersion. These solutions of the generalized nonlinear Schrödinger equation are based on asymptotical methods, first-order perturbation theory, and a renormalization procedure. We have also found an explicit equation for the critical length corresponding to pulse breakup and a criterion which ensure the accuracy of the asymptotic solutions. This criterion is confirmed numerically, showing that the analytical description of the pulses and the critical length formulas developed here for fiber amplifiers and dispersion-decreasing fibers with third-order dispersion are very accurate.

We prove that the analytical expression of the intensity of the relativistic Thomson scattered field for a system composed of an electron interacting with a plane electromagnetic field can be written in the form of a composite periodic function of only one variable, that is, the phase of the incident field. This property is proved without using any approximation in the most general case in which the field is elliptically polarized, the initial phase of the incident field and the initial velocity of the electron are taken into consideration, and the direction in which the radiation is scattered is arbitrary. This property leads to an exact method for calculating the angular and spectral distributions of the scattered field, which reveals a series of physical details of these distributions, such as their dependence on the components of the initial electron velocity. Since the phase of the field is a relativistic invariant, it follows that the periodicity property is also valid when the analysis is made in the inertial system in which the initial velocity of the electron is zero in the case of interactions between very intense electromagnetic fields and relativistic electrons. Consequently, the calculation method can be used for the evaluation of properties of backscattered hard radiations generated by this type of interaction. The theoretical evaluations presented in this paper are in good agreement with the experimental data from literature.

Distributed positive feedback established by a counterpropagating three-wave mixing process in a submicrometer structured second-order nonlinear medium leads to mirrorless parametric oscillation with unusual spectral properties. In this work, we demonstrate experimentally and theoretically that the phase modulation of the pump is coherently transferred to the co-propagating parametric wave, while the counterpropagating wave retains a narrow bandwidth and high coherence. The main mechanisms responsible for these properties are the maximized convective separation between the counterpropagating waves and the associated phase-locking between the pump and the co-propagating parametric wave. This suggests that mirrorless optical parametric oscillators can be pumped with incoherent light and still generate highly coherent backward-propagating radiation.

A numerical study is presented of random lasers as a function of the pumping rate above the threshold for lasing. Depending on the leakiness of the system resonances, which is typically larger in random lasers compared to conventional lasers, we observe that the stationary lasing regime becomes unstable above a second threshold. Coherent instabilities are observed as self pulsation at a single frequency of the output intensity, population inversion, as well as the atomic polarization. We find these Rabi oscillations have the same frequency everywhere in the random laser despite the fact that the field intensity strongly depends on the spatial location.

We report the existence of guided optical solitons of femtosecond duration and nanoscopic mode area. The proposed scheme exploits the structural confinement of light in a low-index subwavelength gap and the nonlinear interaction with a resonantly absorbing medium to achieve stable and ultraconcentrated coherent pulses. Employing full time- and space-dependent Maxwell-Bloch equations, we find that these extremely nonlinear, propagating impulses are quasisolitons, stabilized against dispersion and absorption by self-induced transparency at a laterally constant Rabi frequency.

We consider some new aspects of the formation of moving optical solitons in a medium of Bragg-type resonant grating doped with two-level atoms. For generality, account is taken of the local-field effect assisted by a sufficiently high density of resonant atoms. It is established analytically that there exists a family of soliton solutions to the two-wave Maxwell-Bloch system of equations, with these solitons exhibiting bistable properties. The existence of bistable solitons and their properties are confirmed by numerical simulations.

We apply a recently developed ab initio numerical framework to calculate (generalized) total cross sections for the process of nonsequential (direct) two-photon double ionization of the hydride ion (H${}^{-}$), at photon energies ranging from $7.75$ to $10.5$ eV. The total cross section is about an order of magnitude larger than the corresponding one obtained for helium, the reason being that the electronic correlation is relatively more important in H${}^{-}$. Furthermore, we examine single- and triple-differential cross sections at the photon energies $7.75$ and 9 eV and find that for the lower photon energy the electron energy distribution attains a maximum when both electrons are emitted with equal energies.

We present an indirect imaging method that measures both amplitude and phase information from a transmissive target. Our method is based on an optical eigenmode decomposition of the light intensity and the first-order cross correlation between a target field and these eigenmodes. We demonstrate that such optical eigenmode imaging does not need any a priori knowledge of the imaging system and corresponds to a compressive full-field sampling, leading to high image extraction efficiencies. Finally, we discuss the implications with respect to second-order correlation imaging.

In appropriate ranges of parameters, laser-driven nonlinear optical cavities can support a wide variety of optical patterns, which could be used to carry information. The intensity peaks appearing in these patterns are called cavity solitons and are individually addressable. Using the Lugiato-Lefever equation to model a perfectly homogeneous cavity, we show that cavity solitons can only be located at discrete points and at a minimal distance from the edges. Other localized states which are attached to the edges are identified. By interpreting these patterns in an information coding frame, the information capacity of this dynamical system is evaluated. The results are explained analytically in terms of the the tail characteristics of the cavity solitons. Finally, the influence of boundaries and of cavity imperfections on cavity solitons are compared.

We discuss a class of lasing modes created by a spatially inhomogeneous gain profile. These lasing modes are “extra modes,” in addition to, and very different from, conventional lasing modes, which arise from the passive cavity resonances. These new modes do not have high intensity across the entire gain region, but instead are localized at the gain boundary and throughout the gain-free region. They are surface modes, originating from the transmission resonances of the gain-free region. Using an $S$-matrix description we connect these surface modes to the lasing modes in $\mathcal{P}\mathcal{T}$-symmetric (balanced gain-loss) cavities.

The phenomenon of the total reflection of a weak signal beam from a high-power reference beam due to noncollinear mismatched parametric interaction in a quadratic medium is demonstrated. In a planar geometry the conditions of the signal beam reflection from the optical inhomogeneity induced by the reference beam are found. The analytical expression for the critical value of the signal beam tilt is obtained, and it is shown that total reflection occurs if the initial tilt is less than the critical value. The influence of the walk-off and the reference beam focusing on interaction dynamics are discussed. It is shown that in a bulk medium the beam reflection turns into scattering by an induced inhomogeneity. If reflection conditions are fulfilled, the cylindrical reference beam acts as a convex mirror and lunate distortions of the reflected beam profile occur.

We investigate optomechanical coupling between one-dimensional interacting bosons and the electromagnetic field in a high-finesse optical cavity. We show that by tuning interatomic interactions, one can realize effective optomechanics with mechanical resonators ranging from side-mode excitations of a Bose-Einstein condensate (BEC) to particle-hole excitations of a Tonks-Girardeau (TG) gas. We propose that this unique feature can be formulated to detect the BEC-TG gas crossover and measure the sine-Gordon transition continuously and nondestructively.

The method of complex-coordinate rotation in a finite-element discrete variable representation is implemented to study the photoionization of hydrogen impurity in spherical quantum dots which are modelled by finite oscillator and Gaussian potentials. The level splitting and crossing of hydrogen impurities due to the variation of dot radii and confining potentials are presented, as well as the shifting down of the energy of hydrogenic impurity toward the combined energy of the free hydrogen and the amplitude of the confining potential. We illustrate the staircaselike behavior in ground and excited energy curves varying with dot radii. The variation of photoionization cross sections with photoelectron energies are given for several dot radii. The cross sections as functions of quantum-dot radii and confining potentials for specific photon energies showing resonancelike profiles are observed and discussed.

Electrometry near a dielectric surface is performed using Rydberg electromagnetically induced transparency. The large polarizability of high-$n$-state Rydberg atoms gives this method extreme sensitivity. We show that dipoles produced by adsorbates on the dielectric surface produce a significant electric field that responds to an applied field with a time constant of order 1 s. For transient applied fields (with a time scale of less than 1 s) we observe good agreement with calculations based on numerical solutions of Laplace’s equation using an effective dielectric constant to simulate the bulk dielectric.

We present a theoretical study of isolated attosecond pulse generation with a multicycle chirped and chirped-free two-color field. We show that the bandwidth of the extreme ultraviolet supercontinuum can be extended by combining a multicycle chirped pulse and a multicycle chirped-free pulse. Also, the broadband supercontinuum can still be generated when the macroscopic effects are included. Furthermore, the macroscopic effects can ameliorate the temporal characteristic of the broadband supercontinuum of the single atom, and eliminate the modulations of the broadband supercontinuum. Thus a very smooth broadband supercontinuum and a pure isolated 102-as pulse can be directly obtained. Moreover, the structure of the broadband supercontinuum can be steadily maintained for a relative long distance after a certain distance.